Crack driving force in twisted plywood structures

Twisted plywood architectures can be observed in many biological materials with high fracture toughness, such as in arthropod cuticles or in lamellar bone. Main purpose of this paper is to analyze the influence of the progressive rotation of the fiber direction on the spatial variation of the crack driving force and, thus, on the fracture toughness of plywood-like structures. The theory of fiber composites is used to describe the stiffness matrix of a twisted plywood structure in a specimen-fixed coordinate system. The driving force acting on a crack propagating orthogonally to the fiber-rotation plane is studied by methods of computational mechanics, coupled with the concept of configurational forces. The analysis unfolds a spatial variation of the crack driving force with minima that are beneficial for the fracture toughness of the material. It is shown that the estimation of the crack driving force can be simplified by replacing the complicated anisotropic twisted plywood structure by an isotropic material with appropriate periodic variations of Young's modulus, which can be constructed based either on the local stiffness or local strain energy density variations. As practical example, the concepts are discussed for a specimen with a stiffness anisotropy similar to lamellar bone.

Twisted plywood-like structures exist in many natural fiber composites, such as bone or insect carapaces, and are known to be very fracture resistant. The crack driving force in such materials is analyzed quantitatively for the first time, using the concept of configurational forces. This tool, well established in the mechanics of materials, is introduced to the modeling of biological material systems with inhomogeneous and anisotropic material behavior. Based on this analysis, it is shown that the system can be approximated by an appropriately chosen inhomogeneous but isotropic material for the calculation of the crack driving force. The spatial variation of the crack driving force and, especially, its local minima are essential to describe the fracture properties of twisted plywood structures.